Rough Self-affine Surfaces Research Articles

Friction behaviors of rice husk silica-reinforced elastomer composites in contact with rough self-affine surfaces

This study presents rice husk silica-reinforced elastomer composites fabricated by wet compounding, exhibiting 10% higher dynamic friction coefficients than the reference composites made by conventional dry compounding. Depending on the fabrication method, the filler micro-dispersion was characterized to correlate the measured friction coefficients with the viscoelastic properties with respect to sliding velocity and substrate lubrication. The effect of viscoelastic properties of the elastomer composites on the adhesion and hysteresis friction coefficients was investigated based on the elastomer friction theory. It was found that the constructed friction master curves showed a reasonable correlation with the theory. This study demonstrates that the rice husk silica can be used as a reinforcing filler for sustainable tires. More importantly, the well-dispersed filler microstructures can ensure the higher friction coefficients of the elastomer composites on rough surfaces, improving the tire performances (e.g., wet traction, cornering, and acceleration) of the ever-growing electric vehicles and future mobility.

On the role of scales in contact mechanics and friction between elastomers and randomly rough self-affine surfaces

The paper is devoted to a qualitative analysis of friction of elastomers from the point of view of scales contributing to the force of friction. We argue that – contrary to widespread opinion – friction between a randomly rough self-affine fractal surface and an elastomer is not a multiscale phenomenon, but is governed mostly by the interplay of only two scales – as a rule the largest and the smallest scales of roughness of the contacting bodies. The hypothesis of two-scale character of elastomer friction is illustrated by computer simulations in the framework of the paradigm of Greenwood, Tabor and Grosch using a simplified one-dimensional model.

Maximum micro-slip in tangential contact of randomly rough self-affine surfaces

Many advanced laws of friction contain a characteristic length parameter defining the crossover from sticking to sliding. The physical sense and the scaling properties of this length, however, could not yet be clarified. In the present paper, the fact that any tangential contact of bodies with curved or rough surfaces naturally shows a preliminary slip at the micro scale is used. This is true even if the friction can be described locally by the simplest Coulomb law without preliminary micro-slip. This is suggested as the main physical mechanism for crossover from sticking to sliding. Under this assumption, it becomes possible to theoretically predict the value of the characteristic length of preliminary micro-slip. In this paper, based on recent advances in contact mechanics of self-affine fractal surfaces, the characteristic slip distance for such surfaces is estimated. We show that at low normal forces, the preliminary slip shows no dependence on the system size but only on the applied normal force. For the special case of randomly rough surfaces with a long wavelength roll-off or cut-off the preliminary slip length has the order of magnitude of the rms roughness multiplied with the coefficient of friction.

Method of reduction of dimensionality in contact and friction mechanics: A linkage between micro and macro scales

Abstract Computer simulations have been an integral part of the technical development process for a long time now. Industrial tribology is one of the last fields in which computer simulations have, until now, played no significant role. This is primarily due to the fact that investigating tribological phenomena requires considering all spatial scales from the macroscopic shape of the contact system down to the micro-scales. In the present paper, we give an overview of the previous work on the so-called method of reduction of dimensionality (MRD), which in our opinion, gives a key for the linking of the micro- and macro-scales in tribological simulations. MRD in contact mechanics is based on the mapping of some classes of three-dimensional contact problems onto one-dimensional contacts with elastic foundations. The equivalence of three-dimensional systems to those of one-dimension is valid for relations of the indentation depth and the contact force and in some cases for the contact area. For arbitrary bodies of revolution, MRD is exact and provides a sort of “pocket edition” of contact mechanics, giving the possibility of deriving any result of classical contact mechanics with or without adhesion in a very simple way. A tangential contact problem with and without creep can also be mapped exactly to a one-dimensional system. It can be shown that the reduction method is applicable to contacts of linear visco-elastic bodies as well as to thermal effects in contacts. The method was further validated for randomly rough self-affine surfaces through comparison with direct 3D simulations. MRD means a huge reduction of computational time for the simulation of contact and friction between rough surfaces accounting for complicated rheology and adhesion. In MRD, not only is the dimension of the space reduced from three to one, but the resulting degrees of freedom are independent (like normal modes in the theory of oscillations). Because of this independence, the method is predestinated for parallel calculation on graphic cards, which brings further acceleration. The method opens completely new possibilities in combining microscopic contact mechanics with the simulation of macroscopic system dynamics without determining the “law of friction” as an intermediate step.

Adhesive properties of contacts between elastic bodies with randomly rough self-affine surfaces: A simulation with the method of reduction of dimensionality

Adhesive properties (adhesion force and adhesion coefficient) of contacts between elastic bodies with rough surfaces have been investigated and adhesion maps constructed showing the dependence of adhesive properties on the roughness, rms slope of the surface, elastic modulus, surface energy and fractal dimension. Simulations have been carried out in the frame of the method of reduction of dimensionality.

Scaling relations for contour lines of rough surfaces

Equilibrium and nonequilibrium growth phenomena, e.g., surface growth, generically yields self-affine distributions. Analysis of statistical properties of these distributions appears essential in understanding statistical mechanics of underlying phenomena. Here, we analyze scaling properties of the cumulative distribution of iso-height loops (i.e., contour lines) of rough self-affine surfaces in terms of loop area and system size. Inspired by the Coulomb gas methods, we find the generating function of the area of the loops. Interestingly, we find that, after sorting loops with respect to their perimeters, Zipf-like scaling relations hold for ranked loops. Numerical simulations are also provided in order to demonstrate the proposed scaling relations.

Transport properties of composite solid films with rough self-affine surfaces

We develop a method for computing the ac and dc conductivity ${\ensuremath{\sigma}}_{e}$ of composite films, composed of two types of particles. The films are grown by integrating the Kardar-Parisi-Zhang and the Ginzburg-Landau equations that govern their height and the order parameter. ${\ensuremath{\sigma}}_{e}$ is computed as a function of the film's thickness, frequency, and several relevant morphological parameters. Simulations indicate that the surface roughness strongly affects the films' conductivity. In particular, while ${\ensuremath{\sigma}}_{e}$ exhibits universality if the films' surface is smooth, the universality breaks down with a rough surface. The results also indicate the consistency of the trends in the conductivities with the morphological transitions in the films.

Inversion of roughness parameters of self-affine surfaces from backscattered waves

SUMMARY We propose an inverse method to recover the roughness parameters (altitude rangeh 0, and Hurst exponent H )o fself-affine surfaces from the energy spectrum of backscattered waves. A stochastic forward modelling of the spectrum of the backscattered wavefield averaged along a profile of finite length is proposed in the near-nadir and far-field configuration. A Bayesian formulation of the inverse problem is used to account for the random nature of both the data and the forward problem. An acoustic backscattering experiment is performed with a natural rough self-affine surface for whichh 0 and H are determined through direct measurements of the topography. The inversion of the experimental spectrum of the backscattered acoustic waves shows that a good determination of H is possible, whileh 0 is an unresolved parameter.

Characterization of rough self-affine surfaces by electromagnetic wave scattering

We study the scattering of electromagnetic waves from metallic self-affine surfaces, and review earlier approximative results for the angular distribution of the scattered light (the mean differential reflection coefficient). Furthermore, experimental scattering data for industrial cold-rolled aluminium surfaces that show self-affine scaling invariance are presented. Comparison between these experimental data and approximative analytic and rigorous numerical simulation results shows very good agreement over the dominating angular interval where most of the scattered power is distributed. The excellent quality of this agreement suggests that light scattering can be used as a cheap, robust and versatile (inverse scattering) tool for characterizing self-affine metallic surfaces, i.e. used to estimate roughness exponents as well as topothesies and the related slope parameters.

Fluctuation properties of interfaces and membranes bounded by self-affine surfaces

In this work we study fluctuation properties of fluid interfaces/membranes bounded by a rough self-affine surface. We find that the fractal character of the substrate affects the interface/membrane roughness significantly for healing lengths S\ensuremath{\xi} is the substrate roughness correlation length. However, for healing lengths S\ensuremath{\gg}:\ensuremath{\xi} the rms roughness scales as a power law \ensuremath{\propto}${\mathrm{S}}^{\mathrm{\ensuremath{-}}\mathrm{c}}$ with the exponent c characteristic of the system. Moreover, thermally induced roughness can dominate that induced from the substrate for large healing lengths S (\ensuremath{\gg}:\ensuremath{\xi}) and/or system temperatures T>${\mathrm{T}}_{\mathrm{sc}}$.

Membranes on rough self-affine surfaces.

We study the effective potential Ue between a rough self-affine surface, and a membrane bounded by this surface. We find that the effect of the substrate roughness exponent H on Ue is significant for ζ

Wetting on rough self-affine surfaces.

In this paper, we present a general investigation of the effective potential for complete wetting on self-affine rough surfaces. The roughness effect is investigated by means of the height-height correlation model in Fourier space ~(1+aξ^2q^2)^–1–H. The parameters H and ξ are, respectively, the roughness exponent and the substrate in-plane correlation length. It is observed that the effect of H on the free interface profile is significant for ξ < Y (Y is a “healing” length), and becomes negligible for wetting-layer thickness larger than a characteristic thickness τ~ξ^u for long-range substrate forces. Finally, the large Y (Y»ξ) regime is characterized by a power-law scaling ~Y^–2.